I'm trying to update from phpBB 3.1.8 (new testing board installed on localhost with QiockInastall) to 3.2.0 b2. It went OK until I deleted files which should be deleted. Then I clicked on "Update files" button and installer shows me message in red CANNOT_DELETE_FILES, but all files are already deleted.

Sorry. I'm not sure what are you talking about. You mean File updater method? If yes I tried the first and third method ("Download modified files in an archive" and "Update files via direct file access ("Automatic")) with the same result -> CANNOT_DELETE_FILES.

It doesn't matter if I delete files manually or not, when I use the "Download modified files in an archive" method.

When you use the first option "Download modified files in an archive" you are supposed to delete the files yes (that's the same option as in the old updater).
But the third option "Update files via direct file access ("Automatic")" is new and you are not supposed to do anything else than clicking "continue" the files are added/updated/removed by the updater itself